A local limit law for the empirical spectral distribution of the anticommutator of independent Wigner matrices

Greg W. Anderson

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

Our main result is a local limit law for the empirical spectral distribution of the anticommutator of independent Wigner matrices, modeled on the local semicircle law. Our approach is to adapt some techniques from recent papers of Erdös-Yau-Yin. We also use an algebraic description of the law of the anticommutator of free semicircular variables due to Nica-Speicher, the linearization trick due to Haagerup-Schultz-Thorbjørnsen in a self-adjointness-preserving variant and the Schwinger-Dyson equation. A by-product of our work is a relatively simple deterministic version of the local semicircle law.

Original languageEnglish (US)
Pages (from-to)809-841
Number of pages33
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Volume51
Issue number3
DOIs
StatePublished - Aug 1 2015

Keywords

  • Anticommutators
  • Linearization trick
  • Local semicircle law
  • Schwinger-Dyson equation
  • Stability
  • Wigner matrices

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